Nuclear Physics for Applications

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1 Stanley C. Pruss'm Nuclear Physics for Applications A Model Approach BICENTENNIAL WILEY-VCH Verlag GmbH & Co. KGaA

2 VII Table of Contents Preface XIII 1 Introduction Low-Energy Nuclear Physics for Applications Some General Observations and Notations Overview of Radioactive Decay Processes and Nuclear Reactions Alpha Decay Beta Decay Spontaneous Fission Gamma Decay Nuclear Reactions The Model-basedCharacterofthis Text Sources of Nuclear Data 11 2 Nuclear Masses and Energetics of Radioactive Decay and Nuclear Reactions Introduction Review ofthe Special Theory of Relativity Masses of Atoms and Particles Comments Concerning "Nuclear Stability" and Energetics Spontaneous Transformations and Nuclear Masses Nuclear Stability Bound and Unbound States and Their Energetics: Potential Wells Nuclear and Atomic Masses and Binding Energies ß" Decay ß + Decay or Positron Emission Electron Capture Decay Competitive Decay Modes a Decay Spontaneous Fission Nuclear Reactions 38 Nuclear Physics for Applications. Stanley G. Prussin Copyright 2007 WILEY-VCH Verlag GmbH & Co., Weinheim ISBN:

3 VIIII Table of Contents 3 Phenomenology of Radioactive Decay and Nuclear Reactions Introduction The Phenomenology of Radioactive Decay Units for Describing Radioactive Decay Radioactive Growth and Decay Simple Decay Scheines and Decay Chains Statistical Considerations in Radioactive Decay The Binomial Distribution The Poisson Distribution Application of Statistical Analysis to Common Experimental Conditions Propagation of Errors Reaction Cross Sections 66 4 Nuclear Binding Energies: Empirical Data and the Forces in Nuclei Empirical Masses and Average Binding Energies of Nucleons The Forces Acting Between Nucleons The Average Nuclear Interaction Between Nucleons in the Nucleus and Nuclear Radii Quantization of the Nucleus: Pairing of Identical Nucleons Quantization of the Nucleus: Asymmetry Energy The Semi-Empirical Mass Formula and Applications to Radioactive Decay Introduction The Semi-Empirical Mass Formula The Nuclear Mass Surface The Semi-Empirical Mass Formula and ß Decay The Semi-Empirical Mass Formula and a Decay The Semi-Empirical Mass Formula and Nuclear Fission Discrepancies Between Experimental Masses and those Predicted by the Semi-Empirical Mass Formula Elements of Quantum Mechanics Introduction Elements of Quantum Mechanics The Schrödinger Equation and Conservation Laws Elementary Properties of Operators Elementary Properties of Wave Functions Operators, Eigenfunctions and Conservation Laws Parity Angular Momentum in Quantum Mechanics Operators for Orbital Angular Momentum Angular Momentum and Magnetic Moments 150

4 Table of Contents IIX 6.4 The Vector Model for Angular Momentum The Wave Functions of Many-Particle Systems Nuclear Structure: The Spherical Shell Model Introduction The Independent Particle Model The Angular Equations: Angular Momentum and Parity Some Properties of the Wave Functions The Radial Equation and the Centrifugal Potential Models for the Average Central Potential in the Independent Particle Approximation The Infinite Spherical Potential Well The Isotropie Harmonie Oscillator The Single-Particle Levels of Spherical Nuclei Comparison of the Predictions of the Single-Particle Model with Experiment Nuclear Shapes, Deformed Nuclei and Collective Effects Introduction Collective Excitations Rotational Excitations in (Even,Even) Nuclei Rotational Excitations in Odd-A Nuclei Vibrational Excitations in Nuclei Nuclear Structure in a Deformed Potential The Nilsson Model u Decay and Barrier Penetration Introduction Q a and a Decay Half-Lives Binding of Valence Nucleons and the Potential for Interaction Between an a Particle and a Heavy Nucleus The Wave Functions for Particles in Finite Potential Wells and Barrier Penetration A Simple Model for a Decay Application of the Model to the Decay of Even-Even Nuclei Angular Momentum Effects in et Decay Decay of Odd-A Nuclides and Structure Effects ß Decay Introduction ß Decay and Conservation Laws: The Neutrino and the Weak Interaction The Fermi Golden Rule No The Fermi Theory of Allowed ß Decay ß Spectra 292

5 X I Table of Contents 10.6 Decay Probabilities for ß~ and ß* Decay Some Implications of the Simple Theory of Allowed ß Decay Angular Momentum Effects Nuclear Matrix Elements: Fermi Transitions Nuclear Matrix Elements: Gamow-Teller Transitions Classification ofß Transitions and Experimental Log ]0 ft Electron Caprure Decay X-ray Emission Auger Electron Ejection Elementary Theory of Electron Caprure Ratio of Electron Caprure to Positron Emission ß-Decay Schemes ß-Delayed Particle Emission Comments on Fermi Transitions y Decay and Internat Conversion Introduction The Angular Momentum of Photons and Conservation Laws Introduction to the Theory of Photon Emission The Radiation Field and Matrix Elements for Photon Emission Matrix Elements and Transition Rates Examples of Nuclear Isomerism Some General Observations El Transitions E2 and Ml Transitions Other Transitions Internal Conversion Elementary Theory of Internal Conversion Decay Schemes Nuclear Fission Introduction The Discovery of Nuclear Fission The Liquid-Drop Model and Nuclear Fission: The Nuclear Potential Energy Surface Empirical Data on Spontaneous and Neutron-Induced Fission Energy Release in Fission Fission Fragment Kinetic Energy Kinetic Energy of Prompt Neutrons The Spectrum of Prompt y-rays Summary of the Sources of Energy Release in Fission Fission Barriers and Fission Probabilities 401

6 Table of Contents XI 13 Low-Energy Nuclear Reactions Introduction Kinematics of Nonrelativistic Reactions Kinematics of Elastic Scattering in the Laboratory Coordinate System Kinematics of Elastic Scattering in the Center of Mass Coordinate System Kinematics of General Nonrelativistic Nuclear Reactions Cross Sections for Nuclear Reactions from First-Order Perturbation Theory The Reciprocity Theorem Qualitative Considerations of the Mechanisms of Low-Energy Nuclear Reactions Potential Scattering The Compound Nucleus Direct Reactions The Properties of Time-Dependent States 447 \3.7 A Physical Approach to the Form of Cross Sections for Compound Nucleus Reactions: The Breit-Wigner Single-Level Formula Scattering in Quantum Mechanics: Partial Wave Analysis Extension of the Partial Wave Analysis to Nuclear Reactions S-Wave Scattering and Reactions in the Limit of the Spherical Potential Well Model The Breit-Wigner Single-Level Formula and Experimental Cross Sections About Fission Cross Sections The Interaction of lonizing Radiation with Matter Introduction The Interaction of Photons with Matter Elastic Scattering of Photons on Unbound Electrons Compton Scattering The Photoelectric Effect Pair Production Total Cross Sections and Attenuation Coefficients The Interaction ofcharged Particles with Matter The Stopping of Heavy Charged Particles in Matter The Stopping of Electrons and Positrons in Matter 538 Appendix 1 Atomic Masses 545 Appendix 2 Nuclide Table 565

7 XII I Table of Contents Appendix 3 Physical Constants 607 Appendix 4 First-Order Time-Dependent Perturbation Theory 611 Index 619

An Introduction to. Nuclear Physics. Yatramohan Jana. Alpha Science International Ltd. Oxford, U.K.

An Introduction to. Nuclear Physics. Yatramohan Jana. Alpha Science International Ltd. Oxford, U.K. An Introduction to Nuclear Physics Yatramohan Jana Alpha Science International Ltd. Oxford, U.K. Contents Preface Acknowledgement Part-1 Introduction vii ix Chapter-1 General Survey of Nuclear Properties